In mathematics, a spline is a function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for …

2023年10月5日 · Methods of spline interpolation, including linear, quadratic, and cubic. How spline interpolation avoids some of the pitfalls of higher-order polynomial interpolation.

Throughout our discussion of standard polynomial interpolation, we viewed Pn as a linear space of dimension n + 1, and then expressed the unique interpolating polynomial in several different bases (mono-mial, Newton, Lagrange). The most elegant way to develop spline functions uses the same approach.

Interpolating splines are frequently the functions of choice when it is desired to represent everywhere a function whose values are given exactly only on a finite set of points. Piecewise polynomial functions satisfying other boundary and continuity conditions are also called splines.

A function made up of polynomials that each have a specific interval. In other words a "piecewise polynomial function". Very useful when we want a smooth curve that passes through certain points, such as for matching data, making smooth computer animations, etc.

6 天之前 · A piecewise polynomial function that can have a locally very simple form, yet at the same time be globally flexible and smooth. Splines are very useful for modeling arbitrary functions, and are used extensively in computer graphics.

Use spline to interpolate a sine curve over unevenly-spaced sample points. Use clamped or complete spline interpolation when endpoint slopes are known. To do this, you can specify the values vector y with two extra elements, one at the beginning and one at the end, to define the endpoint slopes.

Spline Interpolation We’ve approached the interpolation problem by choosing (high-degree) polyno-mials for our basis functions φ i: f(x) =! n j=0 c jφ j(x). This approach can be efficient (recall the barycentric form of the Lagrange interpolant), but using high degree poly-

Spline functions are deterministic polynomial functions that perform an interpolation by passing exactly through observation points, calculated over four consecutive points in time or space. They are a local type of interpolation method used to draw appealing curves, often employed in spatial interpolation in the field of geography.

2012年5月3日 · Splines are applied to approximate functions (see Spline approximation; Spline interpolation), and in constructing approximate solutions of ordinary and partial differential equations. They can also be used to construct orthonormal systems with …